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Bean machine · Central Limit Theorem
A physical proof that many small random events add up to a predictable curve. Also called a bean machine or quincunx.
Francis Galton (1822–1911), a British polymath and cousin of Charles Darwin, built this device in the 1890s to show how a normal distribution can emerge from chance. He was studying heredity and variation; the machine made the statistics visible.
Each peg is a nearly fair coin flip: the ball glances left or right. After n rows the landing slot is the number of rightward moves, k. That count follows a binomial distribution, which for large n is indistinguishable from a normal curve.
A real (or simulated) board is not a sequence of independent coin flips. Momentum, bounce, size, and the walls all bias the next collision. That is the point of the sliders:
The overlay in the stats panel is the fair-binomial prediction. When observed mean and σ drift from theory, the board is teaching the difference between a random-walk model and Newtonian collisions.